Frontiers of Quantum Algorithms: From Circuits to Adiabatic Computing

This book provides a deeper exploration of quantum algorithms for graduate students familiar with the basics of quantum information, including Shor's factoring algorithm and Grover's search algorithm. Beyond these early breakthroughs, it covers a wide range of advanced quantum algorithms, highlighting their capabilities and applications. The material is organized into six parts: quantum circuits and gate-based representations, quantum algorithms for algebraic problems such as the hidden subgroup problem, quantum walks as a generalization of random walks for search problems, quantum query complexity and its limits, quantum simulation and applications to linear systems, and adiabatic quantum computing for optimization problems. Collectively, this book demonstrates the rich landscape of quantum computing and its potential to outperform classical methods in diverse computational tasks.